Lesson 3

Balanced Moves

Let's rewrite equations while keeping the same solutions.

Problem 1

In this hanger, the weight of the triangle is \(x\) and the weight of the square is \(y\).

Balanced hanger. Left side, 1 triangle, 3 squares. Right side, 4 triangles, 1 square. 
  1. Write an equation using \(x\) and \(y\) to represent the hanger.

  2. If \(x\) is 6, what is \(y\)?

Problem 2

Andre and Diego were each trying to solve \(2x+6=3x-8\). Describe the first step they each make to the equation.

  1. The result of Andre’s first step was \(\text-x+6=\text-8\).

  2. The result of Diego’s first step was \(6=x-8\).

Problem 3

  1. Complete the table with values for \(x\) or \(y\) that make this equation true: \(3x+y=15\).

    \(x\) 2 6 0 3
    \(y\) 3 0 8

  2. Create a graph, plot these points, and find the slope of the line that goes through them.​​​​

    A blank grid.
(From Unit 3, Lesson 11.)

Problem 4

Match each set of equations with the move that turned the first equation into the second.

Problem 5

Select all the situations for which only zero or positive solutions make sense.


Measuring temperature in degrees Celsius at an Arctic outpost each day in January.


The height of a candle as it burns over an hour.


The elevation above sea level of a hiker descending into a canyon.


The number of students remaining in school after 6:00 p.m.


A bank account balance over a year.


The temperature in degrees Fahrenheit of an oven used on a hot summer day.

(From Unit 3, Lesson 14.)